The high frequency (instantaneous) shear modulus of three-dimensional Yukawa systems is evaluated in a wide parameter range, from the very weakly coupled gaseous state to the strongly coupled fluid at the crystallization point (Yukwa melt). This allows us to quantify how shear rigidity develops with increasing coupling and inter-particle correlations. The radial distribution functions (RDFs) needed to calculate the excess shear modulus have been obtained from extensive molecular dynamics (MD) simulations. MD results demonstrate that fluid RDFs appear quasi-universal on the curves parallel to the melting line of a Yukawa solid, in accordance with the isomorph theory of Roskilde-simple systems. This quasi-universality, allows to simplify considerably calculations of quantities involving integrals of the RDF (elastic moduli represent just one relevant example). The calculated reduced shear modulus grows linearly with the coupling parameter at weak coupling and approaches a quasi-constant asymptote at strong coupling. The asymptotic value at strong coupling is in reasonably good agreement with the existing theoretical approximation.
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